In debates over privatization and global competition mixed Cournot oligopoly models have
been used to show that the presence of a state-owned enterprise in the host country is always
associated with a distortionary effect that may justify privatization even if the public firm is
just as efficient as its private counterparts. This study argues that this result is valid only under
Cournot competition and Cournot competition is not a plausible modelling assumption in this
context because in this type of market the firms’ simultaneous play strategies lack credibility

Cornes, Richard

Sepahvand, Mehrdad

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Mixed Oligopoly, privatization and
strategic trade policy: a note
Mehrdad Sepahvand and Richard Cornes
2005
Online at http://mpra.ub.uni-muenchen.de/3382/
MPRA Paper No. 3382, posted 3. June 2007
Mixed Oligopoly, Privatization and Strategic Trade Policy: a
Note
Richard C. Cornes∗ Mehrdad Sepahvand†
Abstract
In debates over privatization and global competition mixed Cournot oligopoly models have
been used to show that the presence of a state-owned enterprise in the host country is always
associated with a distortionary eﬀect that may justify privatization even if the public firm is
just as eﬃcient as its private counterparts. This study argues that this result is valid only under
Cournot competition and Cournot competition is not a plausible modelling assumption in this
context because in this type of market the firms’ simultaneous play strategies lack credibility.
JEL: D43, L33, L13
Keywords: Privatization, Mixed oligopoly, Strategic Trade Policy
1 Introduction
A standard result in the mixed oligopoly1 literature associates the presence of a public enterprise
in an imperfect market with a distortionary eﬀect that may justify privatization even if the public
firm is as eﬃcient as its private counterparts. The introduction of international competition into
the mixed Cournot oligopoly model leads to a more stronger result. In the presence of foreign
competitors, the host country with a mixed market structure can always improve its welfare by
privatizing the public enterprise and using a production subsidy (Pal and White 1998).
In a discussion of strategic trade policy, Bhagwati (1987) warns readers to be careful about
the findings in that literature because “their policy recommendations are extremely sensitive to
parametric assumptions and the nature of competition”. We believe this warning applies equally to
the mixed oligopoly literature, where the type of competition has a crucial impact on the outcomes.
Nevertheless, researchers who have applied these models have done little to check the robustness of
∗Correspondence address: School of Economics, The University of Nottingham, University Park, NG7
2RD, Tel: +44(0)1159515480; Fax:+44(0)1159514159; Email: richard.cornes@nottingham.ac.uk
†Nottingham University Business School, Jubilee Campus, Walton Road, Nottingham, NG8 1BB, UK.
1A setting where a public firm with an objective that diﬀers from maximizing the firm’s profit competes with a
limited number of private firms in provision of goods and services.
1
their results with respect to the timing assumption or to present a justification for their modeling
assumptions2.
This paper builds on the analysis by Pal and White (1998). We show that privatization improves
welfare only if firms are engaged in Cournot competition. Then we extend the basic quantity-setting
game to a preplay stage where each firm can choose not only the action but also the time of action.
Our findings indicate that adopting a simultaneous play strategy, which is the key assumption of
Cournot model, is inconsistent with the firms’ preferences over the timing of action hence it lacks
credibility. This allows us to provide an alternative explanation for the welfare gain of privatization
in an international Cournot mixed oligopoly model.
2 The Basic Model
Consider a country with a domestic market for a homogeneous good produced by a single state-owned
public firm, m domestic private firms and n foreign private firms. Demand is linear, p = a − Q,
where Q is the total output, Q = qd0 +
Pm
i=1 q
d
i +
Pn
j=1 q
f
j , q
d
0 is the output of the public firm,
qdi , i = 1, ..,m is the output of the i
0th domestic private firm and qfj , j = 1, .., n is the output of the
j0th foreign firm. All firms share an identical production technology represented by a quadratic cost
function, c(q) = c+ (k/2)q2 where k > 0 is a constant. As the number of firms is fixed and we are
not dealing with entry/exit problem, we may set c = 0, with no loss of generality.
The domestic government uses a complete set of trade policy instruments including a subsidy of
s per unit of a domestic firm’s output and an import tariﬀ of t per unit of foreign firm’s output.
If πdi denotes the profit function of i’th domestic private firm and π
f
j denotes the profit function of
j’th foreign firm we have
πdi = [a− (qd0 +
mX
i=1
qdi +
nX
j=1
qfj )]q
d
i − (k/2)(qdi )2 + sqdi i = 1, ..,m, (1)
πfj = [a− (qd0 +
mX
i=1
qdi +
nX
j=1
qfj )]q
f
j − (k/2)(q
f
j )
2 − tqfj j = 1, .., n (2)
The domestic government and public enterprise maximize social welfare, defined as the un-
weighted sum of the consumer surplus plus domestic firms’ profits and tariﬀ revenue less the cost of
the subsidy:
W = CS + πd0 +
mX
i=1
πdi + t
nX
j=1
qfj − s(qd0 +
mX
i=1
qdi ) (3)
where πd0 = p(Q)qd0 − (k/2)qd20 + sqd0 is the public firm’s profit.
We assume a game that constitutes of two phases: regulation phase and action phase. In the
regulation phase, the government anticipating the firms’ behavior in the second phase, commits itself
2Exceptions to this are Pal (1998) Matsumura (2003) and Fjell and Heywood (2004).
2
to selected rates of its policy instruments to maximize domestic welfare. Then in the action phase,
firms compete in quantities knowing the government’s announced policy.
We consider three regimes which diﬀer with respect to the behavior of the public firm and the
timing of its move. Let label N as a standard international oligopoly regime where the public firm
is privatized e.i. it maximizes its own profit, and competes with other firms under Cournot-Nash
assumptions. In a mixed market structure there are two possible settings described and labelled as
follows:
(a) S, for mixed oligopoly with a dominant public firm: the action phase constitutes of two periods.
In period 1, the public firm taking the selected rates of s and t as given sets its output to
maximize (3) anticipating the private firms competition at the later stage. In period 2, m+ n
domestic and foreign private firms choose their outputs to maximize their own profits knowing
the announced levels of s and t and qd0 .
(b) C, for a mixed Cournot oligopoly in which the public firm sets its output simultaneously with
private firms to maximize domestic welfare at the action phase.
3 The Results
Comparison of SPN equilibria in pure strategies in all above regimes leads to the following results:
Proposition 1) In an international mixed Cournot oligopoly with strategic trade policy, privati-
zation of the domestic public enterprise always enhances welfare of the domestic country. However,
if the public enterprise acts as a Stackelberg leader in a quantity-setting game, privatization leaves
unchanged the level of welfare of the domestic country as well as the optimal levels of tariﬀ and
subsidy. Furthermore, with a dominant public enterprise and strategic trade policy at equilibrium
before and after privatization, all domestic firms produce where price is equal to marginal cost.
(See Appendix for the proof).
Fjell and Pal (1996) state that “the marginal cost of the public firm equals the market price if
and only if there is no foreign firm in the domestic market, or n = 0”. As we see in proposition 1,
the public firm may follow marginal cost pricing even in the presence of a foreign firm provided that
a complete set of trade and industrial policies instruments are available that matches all possible
sources of distortion raised by the oligoplistic behavior of private firms. Also proposition 1 demon-
strates the crucial role played by the timing assumption in Pal and White (Propositions 4.1 and
6.2, 1998). It asserts that when the government uses strategic trade policy, privatization improves
welfare of the home country with a mixed market structure only if the public enterprise acts as a
Cournot player. But if it has a first-mover advantage, we cannot expect any gain from privatization.
In other words, the welfare gain of privatization can be fully explained by the timing assumption.
3
4 Towards a Rationale for the Timing Assumption
We focus now on an international mixed oligopoly in its simplest form. There is just one firm of
each type; one domestic public firm, one domestic private firm and one foreign private firm. To
make our model exactly the same as that of Pal and White (1998, Section 3), we set t = 0 i.e. the
home government only uses a production subsidy.
Following Hamilton and Slutsky (1990), consider a hypergame consisting of two stages - a preplay
stage and a basic stage as explained before- in order to study simultaneous versus sequential play
(See Figure 1). In the preplay stage, firms decide at the same time whether to choose actions in the
basic game at the first opportunity and move early, denoted by E, or to wait until observing their
rival’s action and move late, denoted by L. So the set of action times is T = (E,L) and a combination
of timing decisions is ψ ≡ (τ0, τp, τf ) where τ i ∈ T and the subscripts i ∈ {0, p, f} where 0, p and f
stand for domestic public enterprise, domestic private firm and foreign firm respectively. The set of
all possible timings is Ψ.
  
The government 
ob serves the 
announced 
timing of actions, 
ψ , and sets s. 
Firms announced 
moving early, 
observe ψ and s 
and choose qi. 
Firms simultaneously  
choose their time of  
action τi   and 
announce them as  
commitments.   
Firms announced 
moving  late   observe  ψ and s   a n d   q i   a n d   
choose  q j .   
time   
Basic Stage Preplay Stage   
Figure 1: The extended game
The strategy of each firm Si = (τ i, qψi (s)) is the product of T and Φi where Φi is the set of
functions that maps the information set of each firm into the action set of that firm, Ai. Thus the
strategy profile is S = ΠSi.
We do not need to consider all possible strategies of firms at the basic game in order to solve the
game, because Nash equilibrium in subgames eliminates non-equilibrium output choices. Therefore,
we can confine ourselves to Nash equilibria in subgames denoted by eψ. If there exists a unique SNP
equilibrium for the extended game, that would be a self-enforcing equilibrium that Pareto dominates
other feasible strategies at that subgame and dictates the natural order of play in the basic stage.
Proposition 2) In an extended game of international mixed oligopoly with subsidization, the
natural order of play is public Stackelberg leadership game.
4
For simplicity in exposition, suppose α = 10 and k = 1. Although this sounds restrictive, the
results remain valid when α and k take any positive values. Table 1 shows the Nash equilibria in the
subsequent subgames in this simple example.
Table 1: International mixed triopoly: a numerical example
I)Public firm moves early (E)
Foreign Firm
Early Late
Domestic
Private
Firm
E [ 33.96 15.4 1.92 ] [ 34 11.95 2.16 ]
L [ 34.16 14.39 2.03 ] [ 34 15.36 2.16 ]
II) Public firm moves late (L)
Foreign Firm
Early Late
Domestic
Private
Firm
E [ 33.96 10.29 1.92 ] [ 33.96 8.6 1.92 ]
L [ 34.06 15.25 1.92 ] [ 33.96 15.4 1.92 ]
The above payoﬀ matrix shows that the simultaneous play, either in the early period, e(EEE), or
in the later period of the basic game, e(LLL), cannot be the SPN equilibrium: in each one of these
settings there exists at least one player that can unilaterally change its timing of action in a way
that improves its payoﬀs. The SPN equilibrium of the extended game is e(ELL) where the public
firm acts as a Stackelberg leader.
5 Conclusion
The intuition behind the above results is quite simple. If, following the founders of mixed oligopoly
models (Merrill and Schneider, 1966), we consider the public enterprise as an instrument to regulate
an industry from inside, then we should recall that “the necessary assumption is that the government
can credibly commit to its policy choice before the firms make their choices... [this is] reflected by
the assumption that the government moves first in the game tree ” (Brander, 1995).
If the firms’ conduct in an international mixed oligopoly is modelled by a public firm Stackelberg
leadership game, the public firm is an eﬀective policy instrument comparable with a production
subsidy and subsidization is equivalent to the government itself choosing the firm’s output. Therefore
assuming that change in ownership structure has no influence on the firm’s organizational eﬃciency,
5
the home country cannot gain from privatizing an eﬃcient public enterprise and replacing it with a
private firm regulated by a production subsidy.
Bibliography
1. Bhagwati, J. 1987, Essays in International Economic Theory, MIT Press.
2. Brander, J. 1995, Strategic Trade Policy, National Bureau of Economic Research Working
Paper No. 5020.
3. Fjell, K. and J.S. Heywood, 2004, Mixed oligopoly, subsidization and the order of firm’s moves:
the relevance of privatization, Economics Letters, 83, 411-416.
4. Fjell, K. and D. Pal, 1996, A Mixed Oligopoly in the Presence of Foreign Private Firms,
Canadian Journal of Economics, 29, 737-743.
5. Hamilton, J. and S. Slutsky 1990, Endogenous Timing in Duopoly Games: Stackelberg or
Cournot Equilibria, Games and Economic Behavior, 2, 29-49.
6. Matsumara, T. 2003, Stackelberg Mixed Duopoly with Foreign Firm, Bulletin of Economic
Research, 55(3), 275-287.
7. Merrill, W. and N. Schneider, 1966, Government firms in oligopoly industries: a short run
analysis, Quarterly Journal of Economics, 80, 400-412
8. Pal, D., 1998, Endogenous timing in a mixed oligopoly, Economics Letters, 61, 181-185
9. Pal, D. and M. White, 1998, Mixed Oligopoly, Privatization, and Strategic Trade Policy,
Southern Economic Journal, 65(2), 264-281..
Appendix
The model is solved by backward induction. In period 2 of the action phase, maximizing (1) and
(2) simultaneously we obtain the Nash equilibrium output for a given policy instruments s and t,
and the public firm’s output qd0 ,
qdi (q
d
0 , s, t) =
(a− qd0)(k + 1) + s(n+ 1 + k) + tm
(k + 1)(m+ n+ 1 + k)
i = 1, ..,m (4)
qfj (q
d
0 , s, t) =
(a− qd0)(k + 1)− t(m+ 1 + k)− sn
(k + 1)(m+ n+ 1 + k)
j = 1, .., n. (5)
In period 1, the public firm maximizes (3) anticipating the private firms’ behavior in the second
period for a selected rates of s and t. Finally in the regulatory phase, the government, taking into
account how firms react to its policy choice, select s and t to maximize (3). The SPN equilibrium
value of output per domestic firm and the strategic trade policies are:
6
i)qdS0 = q
dS
i =
2a(k + 1)
D
, ii)pS =
2ka (k + 1)
D
, iii)sS =
2a(k + 1)
D
, iv)tS =
ak(k + 1)
D
, (6)
It can be checked that the SPN equilibrium solution of the all-private oligopoly setting is exactly
the same as a mixed oligopoly with dominant public firm.
In the action phase of a mixed Cournot oligopoly, all firms set their outputs simultaneously for
the given rates of t and s. From the simultaneous solution of the FOCs for internal solutions we
have,
qd0(s, t) =
(k + n+ 1)[a(k + 1)− sm]− nmt
(k + 1)Z
(7)
qdi (s, t) =
(k + 1)[ak + s(k + n+ 1) + nt]
(k + 1)Z
i = 1, ..,m (8)
qfj (s, t) =
ka(k + 1)− t[(k + 1)2 + km]− skm
(k + 1)Z
j = 1, .., n (9)
where Z = (k + 1)(k + n + 1) + km. At the first stage of the game, anticipating the equilibrium
behavior of the firms in the next stage, the government maximizes (3) with respect to s, t. The SPN
equilibrium values of these variables are obtained from the solution of the government’s problem
that yields
i)sC =
a(k + 1)[(2(k + 1) + n]
H
, ii)tC =
ak(k + 1)2
H
(10)
where H = 2(k3 + 1) + (2m+ n)(k + 1)2 + 6k(k + 1) +mn. If we plug (10) in (7), (8) and (9), the
SPN equilibrium level of the firms’ outputs are obtained as
i)qdC0 =
a[2(k + 1)2 + k(n+ 1)]
H
, ii)qdCi =
a[2(k + 1)2 + n]
H
, iii)qfCj =
ak(1 + k)
H
. (11)
From (6-i) and (11-i) we can conclude that qdC0 > q
dS
0 and calculating (3) for all scenarios
indicates that WS =WN > WC .
7


Mixed Oligopoly, privatization and strategic trade policy: a note

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveMixed Oligopoly, privatization andstrategic trade policy: a noteMehrdad Sepahvand and Richard Cornes2005Online at http://mpra.ub.uni-muenchen.de/3382/MPRA Paper No. 3382, posted 3. June 2007Mixed Oligopoly, Privatization and Strategic Trade Policy: aNoteRichard C. Cornes∗ Mehrdad Sepahvand†AbstractIn debates over privatization and global competition mixed Cournot oligopoly models havebeen used to show that the presence of a state-owned enterprise in the host country is alwaysassociated with a distortionary effect that may justify privatization even if the public firm isjust as efficient as its private counterparts. This study argues that this result is valid only underCournot competition and Cournot competition is not a plausible modelling assumption in thiscontext because in this type of market the firms’ simultaneous play strategies lack credibility.JEL: D43, L33, L13Keywords: Privatization, Mixed oligopoly, Strategic Trade Policy1 IntroductionA standard result in the mixed oligopoly1 literature associates the presence of a public enterprisein an imperfect market with a distortionary effect that may justify privatization even if the publicfirm is as efficient as its private counterparts. The introduction of international competition intothe mixed Cournot oligopoly model leads to a more stronger result. In the presence of foreigncompetitors, the host country with a mixed market structure can always improve its welfare byprivatizing the public enterprise and using a production subsidy (Pal and White 1998).In a discussion of strategic trade policy, Bhagwati (1987) warns readers to be careful aboutthe findings in that literature because “their policy recommendations are extremely sensitive toparametric assumptions and the nature of competition”. We believe this warning applies equally tothe mixed oligopoly literature, where the type of competition has a crucial impact on the outcomes.Nevertheless, researchers who have applied these models have done little to check the robustness of∗Correspondence address: School of Economics, The University of Nottingham, University Park, NG72RD, Tel: +44(0)1159515480; Fax:+44(0)1159514159; Email: richard.cornes@nottingham.ac.uk†Nottingham University Business School, Jubilee Campus, Walton Road, Nottingham, NG8 1BB, UK.1A setting where a public firm with an objective that differs from maximizing the firm’s profit competes with alimited number of private firms in provision of goods and services.1their results with respect to the timing assumption or to present a justification for their modelingassumptions2.This paper builds on the analysis by Pal and White (1998). We show that privatization improveswelfare only if firms are engaged in Cournot competition. Then we extend the basic quantity-settinggame to a preplay stage where each firm can choose not only the action but also the time of action.Our findings indicate that adopting a simultaneous play strategy, which is the key assumption ofCournot model, is inconsistent with the firms’ preferences over the timing of action hence it lackscredibility. This allows us to provide an alternative explanation for the welfare gain of privatizationin an international Cournot mixed oligopoly model.2 The Basic ModelConsider a country with a domestic market for a homogeneous good produced by a single state-ownedpublic firm, m domestic private firms and n foreign private firms. Demand is linear, p = a − Q,where Q is the total output, Q = qd0 +Pmi=1 qdi +Pnj=1 qfj , qd0 is the output of the public firm,qdi , i = 1, ..,m is the output of the i0th domestic private firm and qfj , j = 1, .., n is the output of thej0th foreign firm. All firms share an identical production technology represented by a quadratic costfunction, c(q) = c+ (k/2)q2 where k > 0 is a constant. As the number of firms is fixed and we arenot dealing with entry/exit problem, we may set c = 0, with no loss of generality.The domestic government uses a complete set of trade policy instruments including a subsidy ofs per unit of a domestic firm’s output and an import tariff of t per unit of foreign firm’s output.If πdi denotes the profit function of i’th domestic private firm and πfj denotes the profit function ofj’th foreign firm we haveπdi = [a− (qd0 +mXi=1qdi +nXj=1qfj )]qdi − (k/2)(qdi )2 + sqdi i = 1, ..,m, (1)πfj = [a− (qd0 +mXi=1qdi +nXj=1qfj )]qfj − (k/2)(qfj )2 − tqfj j = 1, .., n (2)The domestic government and public enterprise maximize social welfare, defined as the un-weighted sum of the consumer surplus plus domestic firms’ profits and tariff revenue less the cost ofthe subsidy:W = CS + πd0 +mXi=1πdi + tnXj=1qfj − s(qd0 +mXi=1qdi ) (3)where πd0 = p(Q)qd0 − (k/2)qd20 + sqd0 is the public firm’s profit.We assume a game that constitutes of two phases: regulation phase and action phase. In theregulation phase, the government anticipating the firms’ behavior in the second phase, commits itself2Exceptions to this are Pal (1998) Matsumura (2003) and Fjell and Heywood (2004).2to selected rates of its policy instruments to maximize domestic welfare. Then in the action phase,firms compete in quantities knowing the government’s announced policy.We consider three regimes which differ with respect to the behavior of the public firm and thetiming of its move. Let label N as a standard international oligopoly regime where the public firmis privatized e.i. it maximizes its own profit, and competes with other firms under Cournot-Nashassumptions. In a mixed market structure there are two possible settings described and labelled asfollows:(a) S, for mixed oligopoly with a dominant public firm: the action phase constitutes of two periods.In period 1, the public firm taking the selected rates of s and t as given sets its output tomaximize (3) anticipating the private firms competition at the later stage. In period 2, m+ ndomestic and foreign private firms choose their outputs to maximize their own profits knowingthe announced levels of s and t and qd0 .(b) C, for a mixed Cournot oligopoly in which the public firm sets its output simultaneously withprivate firms to maximize domestic welfare at the action phase.3 The ResultsComparison of SPN equilibria in pure strategies in all above regimes leads to the following results:Proposition 1) In an international mixed Cournot oligopoly with strategic trade policy, privati-zation of the domestic public enterprise always enhances welfare of the domestic country. However,if the public enterprise acts as a Stackelberg leader in a quantity-setting game, privatization leavesunchanged the level of welfare of the domestic country as well as the optimal levels of tariff andsubsidy. Furthermore, with a dominant public enterprise and strategic trade policy at equilibriumbefore and after privatization, all domestic firms produce where price is equal to marginal cost.(See Appendix for the proof).Fjell and Pal (1996) state that “the marginal cost of the public firm equals the market price ifand only if there is no foreign firm in the domestic market, or n = 0”. As we see in proposition 1,the public firm may follow marginal cost pricing even in the presence of a foreign firm provided thata complete set of trade and industrial policies instruments are available that matches all possiblesources of distortion raised by the oligoplistic behavior of private firms. Also proposition 1 demon-strates the crucial role played by the timing assumption in Pal and White (Propositions 4.1 and6.2, 1998). It asserts that when the government uses strategic trade policy, privatization improveswelfare of the home country with a mixed market structure only if the public enterprise acts as aCournot player. But if it has a first-mover advantage, we cannot expect any gain from privatization.In other words, the welfare gain of privatization can be fully explained by the timing assumption.34 Towards a Rationale for the Timing AssumptionWe focus now on an international mixed oligopoly in its simplest form. There is just one firm ofeach type; one domestic public firm, one domestic private firm and one foreign private firm. Tomake our model exactly the same as that of Pal and White (1998, Section 3), we set t = 0 i.e. thehome government only uses a production subsidy.Following Hamilton and Slutsky (1990), consider a hypergame consisting of two stages - a preplaystage and a basic stage as explained before- in order to study simultaneous versus sequential play(See Figure 1). In the preplay stage, firms decide at the same time whether to choose actions in thebasic game at the first opportunity and move early, denoted by E, or to wait until observing theirrival’s action and move late, denoted by L. So the set of action times is T = (E,L) and a combinationof timing decisions is ψ ≡ (τ0, τp, τf ) where τ i ∈ T and the subscripts i ∈ {0, p, f} where 0, p and fstand for domestic public enterprise, domestic private firm and foreign firm respectively. The set ofall possible timings is Ψ.  The government ob serves the announced timing of actions, ψ , and sets s. Firms announced moving early, observe ψ and s and choose qi. Firms simultaneously  choose their time of  action τi   and announce them as  commitments.   Firms announced moving  late   observe  ψ and s   a n d   q i   a n d   choose  q j .   time   Basic Stage Preplay Stage   Figure 1: The extended gameThe strategy of each firm Si = (τ i, qψi (s)) is the product of T and Φi where Φi is the set offunctions that maps the information set of each firm into the action set of that firm, Ai. Thus thestrategy profile is S = ΠSi.We do not need to consider all possible strategies of firms at the basic game in order to solve thegame, because Nash equilibrium in subgames eliminates non-equilibrium output choices. Therefore,we can confine ourselves to Nash equilibria in subgames denoted by eψ. If there exists a unique SNPequilibrium for the extended game, that would be a self-enforcing equilibrium that Pareto dominatesother feasible strategies at that subgame and dictates the natural order of play in the basic stage.Proposition 2) In an extended game of international mixed oligopoly with subsidization, thenatural order of play is public Stackelberg leadership game.4For simplicity in exposition, suppose α = 10 and k = 1. Although this sounds restrictive, theresults remain valid when α and k take any positive values. Table 1 shows the Nash equilibria in thesubsequent subgames in this simple example.Table 1: International mixed triopoly: a numerical exampleI)Public firm moves early (E)Foreign FirmEarly LateDomesticPrivateFirmE [ 33.96 15.4 1.92 ] [ 34 11.95 2.16 ]L [ 34.16 14.39 2.03 ] [ 34 15.36 2.16 ]II) Public firm moves late (L)Foreign FirmEarly LateDomesticPrivateFirmE [ 33.96 10.29 1.92 ] [ 33.96 8.6 1.92 ]L [ 34.06 15.25 1.92 ] [ 33.96 15.4 1.92 ]The above payoff matrix shows that the simultaneous play, either in the early period, e(EEE), orin the later period of the basic game, e(LLL), cannot be the SPN equilibrium: in each one of thesesettings there exists at least one player that can unilaterally change its timing of action in a waythat improves its payoffs. The SPN equilibrium of the extended game is e(ELL) where the publicfirm acts as a Stackelberg leader.5 ConclusionThe intuition behind the above results is quite simple. If, following the founders of mixed oligopolymodels (Merrill and Schneider, 1966), we consider the public enterprise as an instrument to regulatean industry from inside, then we should recall that “the necessary assumption is that the governmentcan credibly commit to its policy choice before the firms make their choices... [this is] reflected bythe assumption that the government moves first in the game tree ” (Brander, 1995).If the firms’ conduct in an international mixed oligopoly is modelled by a public firm Stackelbergleadership game, the public firm is an effective policy instrument comparable with a productionsubsidy and subsidization is equivalent to the government itself choosing the firm’s output. Thereforeassuming that change in ownership structure has no influence on the firm’s organizational efficiency,5the home country cannot gain from privatizing an efficient public enterprise and replacing it with aprivate firm regulated by a production subsidy.Bibliography1. Bhagwati, J. 1987, Essays in International Economic Theory, MIT Press.2. Brander, J. 1995, Strategic Trade Policy, National Bureau of Economic Research WorkingPaper No. 5020.3. Fjell, K. and J.S. Heywood, 2004, Mixed oligopoly, subsidization and the order of firm’s moves:the relevance of privatization, Economics Letters, 83, 411-416.4. Fjell, K. and D. Pal, 1996, A Mixed Oligopoly in the Presence of Foreign Private Firms,Canadian Journal of Economics, 29, 737-743.5. Hamilton, J. and S. Slutsky 1990, Endogenous Timing in Duopoly Games: Stackelberg orCournot Equilibria, Games and Economic Behavior, 2, 29-49.6. Matsumara, T. 2003, Stackelberg Mixed Duopoly with Foreign Firm, Bulletin of EconomicResearch, 55(3), 275-287.7. Merrill, W. and N. Schneider, 1966, Government firms in oligopoly industries: a short runanalysis, Quarterly Journal of Economics, 80, 400-4128. Pal, D., 1998, Endogenous timing in a mixed oligopoly, Economics Letters, 61, 181-1859. Pal, D. and M. White, 1998, Mixed Oligopoly, Privatization, and Strategic Trade Policy,Southern Economic Journal, 65(2), 264-281..AppendixThe model is solved by backward induction. In period 2 of the action phase, maximizing (1) and(2) simultaneously we obtain the Nash equilibrium output for a given policy instruments s and t,and the public firm’s output qd0 ,qdi (qd0 , s, t) =(a− qd0)(k + 1) + s(n+ 1 + k) + tm(k + 1)(m+ n+ 1 + k)i = 1, ..,m (4)qfj (qd0 , s, t) =(a− qd0)(k + 1)− t(m+ 1 + k)− sn(k + 1)(m+ n+ 1 + k)j = 1, .., n. (5)In period 1, the public firm maximizes (3) anticipating the private firms’ behavior in the secondperiod for a selected rates of s and t. Finally in the regulatory phase, the government, taking intoaccount how firms react to its policy choice, select s and t to maximize (3). The SPN equilibriumvalue of output per domestic firm and the strategic trade policies are:6i)qdS0 = qdSi =2a(k + 1)D, ii)pS =2ka (k + 1)D, iii)sS =2a(k + 1)D, iv)tS =ak(k + 1)D, (6)It can be checked that the SPN equilibrium solution of the all-private oligopoly setting is exactlythe same as a mixed oligopoly with dominant public firm.In the action phase of a mixed Cournot oligopoly, all firms set their outputs simultaneously forthe given rates of t and s. From the simultaneous solution of the FOCs for internal solutions wehave,qd0(s, t) =(k + n+ 1)[a(k + 1)− sm]− nmt(k + 1)Z(7)qdi (s, t) =(k + 1)[ak + s(k + n+ 1) + nt](k + 1)Zi = 1, ..,m (8)qfj (s, t) =ka(k + 1)− t[(k + 1)2 + km]− skm(k + 1)Zj = 1, .., n (9)where Z = (k + 1)(k + n + 1) + km. At the first stage of the game, anticipating the equilibriumbehavior of the firms in the next stage, the government maximizes (3) with respect to s, t. The SPNequilibrium values of these variables are obtained from the solution of the government’s problemthat yieldsi)sC =a(k + 1)[(2(k + 1) + n]H, ii)tC =ak(k + 1)2H(10)where H = 2(k3 + 1) + (2m+ n)(k + 1)2 + 6k(k + 1) +mn. If we plug (10) in (7), (8) and (9), theSPN equilibrium level of the firms’ outputs are obtained asi)qdC0 =a[2(k + 1)2 + k(n+ 1)]H, ii)qdCi =a[2(k + 1)2 + n]H, iii)qfCj =ak(1 + k)H. (11)From (6-i) and (11-i) we can conclude that qdC0 > qdS0 and calculating (3) for all scenariosindicates that WS =WN > WC .7

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Mixed Oligopoly, privatization and strategic trade policy: a note

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